Application of Quantum Approximate Optimization to Reduced Order Modeling

Quantum computing is an advancing area of research in which computer hardware and algorithms are developed to take advantage of quantum mechanical phenomena. In recent studies, quantum algorithms have shown promise in solving linear systems of equations. Reduced-order modeling (ROM) algorithms for studying fluid dynamics has shown success in identifying linear operators that can describe flowfields. Dynamic mode decomposition (DMD) is a particularly useful method in which a linear operator is identified from data. In this work, DMD is reformulated as an optimization problem to propagate the state of the linearized dynamical system on a quantum computer. Quadratic Unconstrained Binary Optimization (QUBO), a technique for optimizing quadratic polynomials in binary variables, allows for quantum annealing algorithms to be applied. A quantum circuit model (Quantum Approximation Optimization Algorithm, QAOA) is utilized. Results are shown for predictions made by QUBO and QAOA on flow over a 2D cylinder at Re = 220 and flow over a NACA0009 airfoil at Re = 500 and α = 15°. The quantum-ROM predictions are found to depend on the precision. Comparisons with DMD predictions from a classical computer algorithm are made, as well as an analysis of relevant speedups and computational complexity.